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A tree π -base for * without cofinal branches

Fernando Hernández-Hernández (2005)

Commentationes Mathematicae Universitatis Carolinae

We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree π -base for * with no ω 2 branches yet of height ω 2 . We establish that this is also possible for * using a natural modification of Mathias forcing.

Almost maximal topologies on groups

Yevhen Zelenyuk (2016)

Fundamenta Mathematicae

Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

We introduce the notion of a coherent P -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a P -point on ω , and show that these ultrafilters exist generically under 𝔠 = 𝔡 . This improves the known existence result of Ketonen [On the existence of P -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1, 233–241] can...

Completeness properties of function rings in pointfree topology

Bernhard Banaschewski, Sung Sa Hong (2003)

Commentationes Mathematicae Universitatis Carolinae

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

Coronas of ultrametric spaces

Igor V. Protasov (2011)

Commentationes Mathematicae Universitatis Carolinae

We show that, under CH, the corona of a countable ultrametric space is homeomorphic to ω * . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.

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